Coupled Cluster Linear Response Theory Research Articles

X-ray and UV Spectra of Glycine within Coupled Cluster Linear Response Theory.

The coupled cluster models CCSD and CC3 are used to investigate the (core) excited states and ionization energies of glycine in the gas phase. Excited states and ionization energies in the UV spectral range are calculated using a standard coupled cluster linear response, while core-level excited states and ionization potentials are calculated using the core-valence separation approximation. The temperature dependence from different conformers is also assessed.

Near-Edge X-ray Absorption Fine Structure within Multilevel Coupled Cluster Theory.

Core excited states are challenging to calculate, mainly because they are embedded in a manifold of high-energy valence-excited states. However, their locality makes their determination ideal for local correlation methods. In this paper, we demonstrate the performance of multilevel coupled cluster theory in computing core spectra both within the core-valence separated and the asymmetric Lanczos implementations of coupled cluster linear response theory. We also propose a visualization tool to analyze the excitations using the difference between the ground-state and excited-state electron densities.

Communication: X-ray absorption spectra and core-ionization potentials within a core-valence separated coupled cluster framework.

We present a simple scheme to compute X-ray absorption spectra (e.g., near-edge absorption fine structure) and core ionisation energies within coupled cluster linear response theory. The approach exploits the so-called core-valence separation to effectively reduce the excitation space to processes involving at least one core orbital, and it can be easily implemented within any pre-existing coupled cluster code for low energy states. We further develop a perturbation correction that incorporates the effect of the excluded part of the excitation space. The correction is shown to be highly accurate. Test results are presented for a set of molecular systems for which well converged results in full space could be generated at the coupled cluster singles and doubles level of theory only, but the scheme is straightforwardly generalizable to all members of the coupled cluster hierarchy of approximations, including CC3.

Frozen-Density Embedding Potentials and Chiroptical Properties.

The efficacy of the frozen density embedding (FDE) approach to the simulation of solvent effects is examined for two key chiroptical properties-specific rotation and circular dichroism spectra. In particular, we have investigated the performance of a wave function-theory-in-density-functional-theory (WFT-in-DFT) FDE approach for computing such properties for the small, rigid chiral compound (P)-dimethylallene interacting with up to three water molecules. Although the solvent potential is obtained through DFT, the optical response is computed using coupled cluster linear response theory for mixed electric and magnetic field perturbations. We find that the FDE potential generally yields too small a shift from the isolated molecule as compared to that introduced by the explicit solvent. In one case, the FDE potential fails to reproduce a change in sign of the ORD in which the solute interacts with two solvent molecules. The source of these errors is due primarily to the lack of solvent response to the external field and is analyzed in terms of solvent-solute charge transfer excitations.

Reappraisal of Nuclear Quadrupole Moments of Atomic Halogens via Relativistic Coupled Cluster Linear Response Theory for the Ionization Process

The coupled cluster based linear response theory (CCLRT) with four-component relativistic spinors is employed to compute the electric field gradients (EFG) of (35)Cl, (79)Br, and (127)I nuclei. The EFGs resulting from these calculations are combined with experimental nuclear quadrupole coupling constants (NQCC) to determine the nuclear quadrupole moments (NQM), Q of the halide nuclei. Our estimated NQMs [(35)Cl = -81.12 mb, (79)Br = 307.98 mb, and (127)I = -688.22 mb] agree well with the new atomic values [(35)Cl = -81.1(1.2), (79)Br = 302(5), and (127)I = -680(10) mb] obtained via Fock space multireference coupled cluster method with the Dirac-Coulomb-Breit Hamiltonian. Although our estimated Q((79)Br) value deviates from the accepted reference value of 313(3) mb, it agrees well with the recently recommended value, Q((79)Br) = 308.7(20) mb. Good agreement with current reference data indicates the accuracy of the proposed value for these halogen nuclei and lends credence to the results obtained via CCLRT approach. The electron affinities yielded by this method with no extra cost are also in good agreement with experimental values, which bolster our belief that the NQMs values for halogen nuclei derived here are reliable.

Application of relativistic coupled cluster linear response theory to helium-like ions embedded in plasma environment

Ionization potential and low lying 1S01P1 excitation energies (EE) of highly stripped He-like ions C4 +, Al11 +, and Ar16 + embedded in plasma environment are calculated for the first time using the state-of-the-art coupled cluster (CC)-based linear response theory (LRT) with the four-component relativistic spinors and compared with available experimental data from laser plasma experiments. Debye's screening model is used to estimate the effect of plasma on the ions within the relativistic and non-relativistic framework. The transition energies computed at the CCLRT level using the Debye model agree well with experiment and with other available theoretical data. To our knowledge, no prior CCLRT calculations within the Dirac–Fock framework are available for these systems. Our calculated transition energies for helium-like ions are in accord with experiment; we trust that our predicted EE might be acceptably good for the systems considered. Our preliminary result indicates that CCLRT with the four-component relativistic spinors appears to be a valuable tool for studying the atomic systems where accurate treatments of correlation effects play a crucial role in shaping the spectral lines of ions subjected to plasma environment.

Calculation of Dipole Transition Matrix Elements and Expectation Values by Vibrational Coupled Cluster Method.

An effective operator approach based on the coupled cluster method is described and applied to calculate vibrational expectation values and absolute transition matrix elements. Coupled cluster linear response theory (CCLRT) is used to calculate excited states. The convergence pattern of these properties with the rank of the excitation operator is studied. The method is applied to a water molecule. Arponen-type double similarity transformation in extended coupled cluster (ECCM) framework is also used to generate an effective operator, and the convergence pattern of these properties is compared to the normal coupled cluster (NCCM) approach. It is found that the coupled cluster method provides an accurate description of these quantities for low lying vibrational excited states. The ECCM provides a significant improvement for the calculation of the transition matrix elements.

On the importance of vibrational contributions to small-angle optical rotation: Fluoro-oxirane in gas phase and solution

The specific optical rotation of (S)-fluoro-oxirane in gas phase and solution is predicted using time-dependent density functional theory (B3LYP functional) and coupled cluster linear response theory. Upon vibrational averaging, the coupled cluster singles and doubles model predicts the gas phase specific optical rotation to be 8.1 degrees (dm g/cm(3))(-1) at 355 nm at room temperature. This is an order of magnitude smaller than the B3LYP result of 68.4 degrees (dm g/cm(3))(-1). The main source of this discrepancy is the electronic contribution at the equilibrium geometry. The effects of cyclohexane and acetonitrile solvents are calculated for both the electronic and vibrational contributions with the B3LYP functional. The specific optical rotation is estimated to change significantly depending on the polarity of the solvent, increasing in cyclohexane and decreasing in acetonitrile.

Calculation of vibrational energy of molecule using coupled cluster linear response theory in bosonic representation: Convergence studies

Vibrational excited state energies have been calculated using vibrational coupled cluster linear response theory (CCLRT). The method has been implemented on formaldehyde and water molecule. Convergence studies have been shown with varying the cluster operator from S(4) to S(6) as well as the excitation operator from four bosons to six bosons. A good agreement with full configuration interaction results has been observed with S(6) truncation at coupled-cluster method level and six bosonic excitations at CCLRT level.

A Comparison of Møller-Plesset and Coupled Cluster Linear Response Theory Methods for the Calculation of Dipole Oscillator Strength Sum Rules and C6 Dispersion Coefficients

Four correlated linear response theory methods - the second order polarization propagator approximation (SOPPA), the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes, SOPPA(CCSD), the CC2 and coupled cluster singles doubles (CCSD) linear response theory - were used to determine the dipole oscillator strength sum rules of the hydrogen halides HX (with X = F, Cl, Br and I) and the C6 dispersion coefficient for all pairs of interacting HX molecules via numerical integration of the Casimir-Polder formula. The dependence of the polarizabilities, their frequency dependence and the C6 coefficients on the level of correlation and the dependence of the C6 coefficients on the two intramolecular bond lengths were studied.

The Current State of Ab Initio Calculations of Optical Rotation and Electronic Circular Dichroism Spectra

The current ability of ab initio models to compute chiroptical properties such as optical rotatory dispersion and electronic circular dichroism spectra is reviewed. Comparison between coupled cluster linear response theory and experimental data (both gas and liquid phase) yields encouraging results for small to medium-sized chiral molecules including rigid species such as (S)-2-chloropropionitrile and (P)-[4]triangulane, as well as conformationally flexible molecules such as (R)-epichlorohydrin. More problematic comparisons are offered by (S)-methyloxirane, (S)-methylthiirane, and (1S,4S)-norbornenone, for which the comparison between theory and experiment is much poorer. The impact of basis-set incompleteness, electron correlation, zero-point vibration, and temperature are discussed. In addition, future prospects and obstacles for the development of efficient and reliable quantum chemical models of optical activity are discussed, including the problem of gauge invariance, scaling of the coupled cluster approach with system size, and solvation.

Dipole moments of open-shell radicals using an analytic linear response approach in the Fock space multi-reference coupled cluster method

We report molecular response properties of open-shell doublet radicals, obtained analytically using Fock space multi-reference coupled-cluster linear response theory wherein the radicals described can be treated as electron-attached states of closed-shell cations. In particular, we report the dipole moments of CH, SiH and NO radicals and the corresponding cations. The results have been compared with finite-field Fock space multi-reference coupled-cluster results using relaxed orbitals as well as those obtained using single-reference coupled cluster based response theory, and with experimental numbers.

Generalization of coupled-cluster response theory to multireference expansion spaces: application of the coupled-cluster singles and doubles effective Hamiltonian

Employing separate cluster ansatz in time-independent and time-dependent wave-operators, coupled-cluster (CC) response theory is generalized to multireference (MR) expansion spaces. For state energies, this corresponds to the MR secular problem with an arbitrary similarity-transformed effective Hamiltonian, H˜=Ω−1HΩ. The effective Hamiltonian can be generated via size-extensive CC methods. Thus the states in MR linear response theory (MRLRT) maintain the usual CC core-extensive properties. We have used the Gelfand unitary group basis of the spin-adapted configurations to construct the matrix of H˜ in the MR excitation space. As a preliminary application, the CC singles and doubles effective Hamiltonian is applied to excitation and photoionization energies of the CH+ and N2 molecules, and is compared with experimental results and results from other numerical procedures including conventional CC linear response theory (CC-LRT), MR and full configuration interaction (MRCI and FCI) methods. The numerical results indicate that MRLRT reproduces valence and external excited states quantitatively, combining the best features of CC-LRT and MRCI.

Gauge invariance of the coupled cluster oscillator strength

We present an ab initio study of gauge invariance within coupled cluster linear response theory, exemplified by the electric dipole oscillator strength. Through sample calculations using H 2, Ne, N 2 and H 2O as model systems, it is demonstrated that the coupled cluster singles and doubles (CCSD) method, in conjunction with augmented basis sets, provides a reasonable agreement between length, velocity and mixed gauge electronic oscillator strengths.

Cauchy moments and dispersion coefficients using coupled cluster linear response theory

Expressions for the even Cauchy moments for nonvariational methods have been derived using the time-averaged quasienergy Lagrangian technique. The expressions obtained require the solution of linear equations but do not involve a sum over individual excited-state contributions. An implementation is reported for the coupled cluster models CCS, CC2, and CCSD and calculations have been performed for the Cauchy moments and the Verdet and Cotton–Mouton constants of the Ne atom and for the C6 dispersion coefficient of the Ne2 dimer.

Dynamic CCSD polarisabilities of CHF 3 and CHCl 3

The frequency dependent polarisabilities of fluoroform and chloroform are calculated using coupled cluster linear response theory for a range of frequencies in the visible spectrum. The results are compared with SCF and with experimental values.

Coupled cluster approach to the single-particle Green's function

Diagrammatic and Coupled Cluster techniques are used to develop an approach to the single-particle Green's function G which concentrates on G directly rather than first approximating the irreducible self-energy and then solving Dyson's equation. As a consequence the ionization and attachment parts of the Green's function satisfy completely decoupled sets of equations. The proposed Coupled Cluster Green's Function method (CCGF) is intimately connected to both Coupled Cluster Linear Response Theory (CCLRT) and the Normal Coupled Cluster Method (NCCM). These relations are discussed in detail. © 1992 John Wiley & Sons, Inc.